Old Tom confronted a unsolvable riddle. His apple orchard – 16 plots arranged in a perfect 4×4 grid – needed distribution among his three sons before his health deteriorated .
The task appeared simple: eldest son Jake merited 7 plots for his fifteen years of labor, middle son Marcus earned 6 plots after eight years of assistance, and youngest Peter deserved 3 plots despite laboring two summers.
But here lay the twist that baffled everyone: each son’s legacy had to form one connected piece of land. No scattered plots. Each portion had to create a single unbroken shape where one could walk from any plot to any other within that son’s territory.
Tom drew combinations for hours. His neighbor Bill claimed it unfeasible. His wife Martha filled pages with unsuccessful tries over two days. Even Jake quick with figures, surrendered after a week.
“There’s no way to squeeze 7 linked parts, 6 linked parts, and 3 linked parts onto a 4×4 grid,” was the consensus among everyone.
Tom stood his ground. Fragmented parcels would create farming headaches and endless property line conflicts. As the sun dipped below the horizon on day ten, he experienced a moment of clarity that cracked the puzzle everyone had struggled with for weeks.
Can you work out how Tom split the 16 sections between his three sons ensuring each inheritance remained in one piece?
Challenge: Sketch a 4×4 grid and attempt to divide it into three connected shapes of 7, 6, and 3 squares each. Keep in mind: connected means you can move between squares going up down, left, or right – diagonal moves don’t count.
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SOLUTION:
The solution was to create more creative, interlocking patterns like following:
J J J M
J J P M
J P P M
J M M M
Where:
- J = Jake (7 sections): Forms an inverted L-shape along the left side and top
- M = Marcus (6 sections): Creates a backwards L-shape on the right and bottom
- P = Peter (3 sections): Gets a small connected block in the middle
Each son’s land is perfectly connected, and the numbers work out exactly: 7 + 6 + 3 = 16 sections.